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If you start with the following equation of an ellipse:

x2/4 + y2/9 = c2

and transform the equation to

9x2/36 + 4y2/36 = 36c2

the denominators are the same but the equation is unchanged and so the ellipse remains exactly as it was before.

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Q: What happens to the shape of an ellipse when the denominators are the same?
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